Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
NOBLE GASES AND EVOLUTION OF THE
ATMOSPHERE
INTRODUCTION
Just as variations in the isotopic composition of radiogenic incompatible elements provides some information about the flux of incompatible elements from mantle to crust through time, variations in
the isotopic composition of radiogenic atmophile elements provide information about the flux of
these element from mantle to atmosphere through time. A number of radiogenic decay products are
noble gases that are concentrated in the atmosphere. These include 40Ar and 4He, which are produced
by beta decay of 40K and alpha decay of U and Th respectively, and 84K and 86Kr, 131Xe, 132Xe, 134Xe, and
136
Xe produced by spontaneous fission of U and Th. In addition, 129Xe is the decay product of the extinct
radionuclide 129I (half life: 17 Ma) and other Xe isotopes were produced by fission of the extinct nuclide 244Pu (half life 82 Ma). Finally, 21Ne is ‘nucleogenic’, it can be produced by reaction between ‘fissogenic’ neutrons and magnesium as well as between alpha particles and 18O.
HE AND OTHER NOBLE GASES IN THE EARTH
As usual, we need first to examine the available data set before attempting to draw any inferences.
In this particular case, the data of interest consists the isotopic composition of atmospheric gases and
gases from submarine-erupted basalts and some deep wells. When basalts are erupted subareally, t h e
gaseous elements exsolve from the melt and are lost to the atmosphere. Solubility of volatile compounds in a silicate melt is a strong function of pressure. When basalts are erupted under several
kilometers of seawater, the solubility is such that at least some of the gases remain in the melt and
are trapped in the quenched glassy rims of pillow basalts. Noble gases in the continental crust are
generally at low concentration and furthermore, are dominated by radiogenic components. Thus the
two main reservoirs of noble gases in the Earth are the atmosphere and the mantle. Figure 25.1 summarizes the variations in isotope ratios of atmophile elements observed in MORB, and one set of OIB,
namely basalts from the young Hawaiian seamount Loihi. The data set is rather limited, partly because of the scarcity of samples from young seamounts, but also because of the difficulty of the measurements. Measurement of the isotopic composition of xenon is particularly difficult and the data set
is there for quite limited.
Noble gases in the atmosphere have uniform isotope ratios, which are listed in Table 25.1, and
they thus provide a good reference against which mantle values can be compared. While some workers adhere to the usual convention of placing the radiogenic isotope in the numerator, most report t h e
3
He/4He (hence the convention for He isotopes is to defy the convention). Most often, He isotope ratios are reported relative to the atmospheric value in the R/RA notation:
Ê 3 He ˆ
( 3 He /4 He)sample
= 3
Á4 ˜
4
Ë He ¯ R / R A ( He / He) atmosphere
†
25.1
However, some workers report the 4He/3He ratio.
In these units, crustal rocks generally have He
isotope ratios in the range of 0.01 to 1 while
mantle-derived rocks have values in the range
of 5 to 40. Low values in the crust reflect degassing of He that occurred during their formation and the subsequent production of 4He by ra179
Table 25.1. Atmospheric Noble Gas Isotope Ratios
Isotope Ratio
Value in the Atmosphere
3
He/4He
1.39 ¥ 10-6
4
3
He/ He
7.19 ¥ 105
21
20
Ne/ Ne
0.00296
22
Ne/20Ne
0.102
40
Ar/36Ar
295.5
129
Xe/130Xe
6.496
132
Xe/130Xe
6.607
134
Xe/130Xe
2.563
136
Xe/130Xe
2.176
4/1/03
Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
7.2
E
E
E
r=.1
129Xe
130Xe
E
.2 .3
6.8
E
JJ J
1
J
2
2.8
E
E
E
E
J JE
E
J
E
EE
EE
EJ
EJE
E
JJJ
E
JJ
O
O
ZO
J
134Xe
130Xe
3
O
6.4
J
Z
O
O
a
10
¥ 103
100
4He
3He
atmosphere
old oceanic crust
J sediments
J
J
E
J
60 0.01JJJJJE JJ
J
¥10 3
20
40Ar/40Ar
.1
7.0
7.6
2.8
JE E E
JE EJJ
JJ
E
E
E
b
10
6.4
c
129Xe/130Xe
E
E E
O
O
O
20 O
2.6
40Ar/ 40Ar
20
¥10 3
134Xe
130Xe
2.6
EE
E1
E E 2
JEE
E
JJ J E
E
J
J E
r=.1
.3
4
d
O
Z
J
10
20
40Ar/ 40Ar
¥10 3
Figure 25.1 Isotope ratios of noble gases in the mantle as sampled by oceanic basalts.
Symbols are: O Loihi seamount, J Indian Ocean MORB, E Atlantic MORB; Z a i r
(from Allégre et al., 1986).
dioactive decay. Higher 3He/4He in mantle-derived rocks indicates that the mantle has not been entirely degassed and retains at least a part of its initial, or primordial, inventory of noble gases. He is
unique in that it is the only element that is lost from the Earth in significant quantities. This is because it light enough that some fraction of He atoms reach escape velocity in the upper atmosphere
(while H is lighter, almost all H in the atmosphere is present as H 2O, which is too heavy to reach
escape velocity). The residence time of He in the atmosphere is not known exactly; however, it is
quite short, geologically speaking, probably no more than a few million years. The isotopic composition of He in the atmosphere thus reflects the isotopic composition of He leaking from the solid
Earth, and is therefore intermediate between the crust and mantle values.
What the data show is that MORB has high 40Ar/36Ar, 129Xe/130Xe, 134Xe/130Xe and low 4He/3He ratios relative to the atmosphere, while some OIB, notably those from Hawaii, have low 4He/3He,
40
Ar/36Ar, 129Xe/130Xe, and 134Xe/130Xe relative to MORB. Relative to the atmosphere, basalts from
Loihi, the youngest volcano in the Hawaiian chain, have low 4He/3He and high 40Ar/36Ar and
slightly higher 134Xe/130Xe, while 129Xe/130Xe is the same as the atmosphere (Figure 25.1). Because
He is continually lost, its atmospheric concentration is quite low and contamination of basalts by a t mosphere, or fluids that have equilibrated with the atmosphere, is minimal. This is not the case for
other noble gases, thus resolving and correcting for atmospheric contamination is a difficult problem.
The trends apparent in Figure 25.1a, 25.1c, and 25.1d may reflect, in whole or in part, atmospheric
contamination.
Figure 25.2 shows the isotopic composition of He in basalts from a variety of mantle plumes plotted
as a function of plume flux estimates of Davies (1988) and Sleep (1990). As may be seen, there is no
180
4/1/03
Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
obvious relationship between plume flux and He isotopic composition. He isotopic ratios in plumes
vary widely, and can be both higher and lower than the MORB value, although most are higher. In
contrast, MORB has a relatively uniform He isotope ratio of 8.75 ±2.14 (R/RA ) .
The generally higher 3He/4He ratios in mantle plumes provide evidence that they are derived
from a part of the mantle that has been less degassed that the mantle that gives rise to MORB. The
latter is generally assumed to be the upper mantle or asthenosphere. Simple logic suggests that t h e
deep mantle should have experience less melting and degassing than the upper mantle (because melting and degassing can occur only
40
near the surface). Hence, high
Pacific
He isotope ratios in plumeHawaii
derived basalts is often cited as
Atlantic
(Loihi)
evidence that plumes come from
30
Indian
the deep mantle. Once must be
Continental
careful, however.
Since the
3He
Earth is not a simple place, sim4He
ple logic might be misleading.
20 Heard/Kerguelen Societies
Low 3He/4He ratios in some
Juan
Fernandez
(R/RA)
CV
plumes, such as Tristan and St.
Reunion CookHelena, could reflected the presPitcairn Australs
ence or predominance of material
10 Canaries
MORB
recycled from the Earth’s surface,
Tristan/
such as oceanic crust, in these
Marquesas (Davies, 1988)
Gough
plumes.
There is an inherent inconsis0
5
10
15
tency between He and non-noble
gas radiogenic isotope ratios in
mantle-derived basalts. Overall,
Iceland
there is little correlation between
40
He isotope ratios and other isoHawaii
tope ratios, such as 87Sr/86Sr, as is
(Loihi)
illustrated in Figure 25.3 ( a l though correlations often exist
30
Galapagos
within individual oceanic islands). Furthermore, the highest
3 He
Samoa
3
He/4He ratios are associated
4He
20
with intermediate 87Sr/86Sr,
Afar
143
Nd/144Nd, and Pb isotope ratios
(R/RA) ASP Yellowstone
(Figure 25.3).
These high
Bouvet
3
Easter
He/4He ratios suggest that this
Azores Cook-Australs
material has been substantially
10
MORB
less degassed than material with
St. Helena Marquesas
lower 3He/4He ratios. On the
(Sleep, 1990)
other hand, isotope ratios such as
87
Sr/86S r associated with these
0
5
10
15
highest 3He/4He ratios indicated
these plumes consist of material
Plume Flux (km3/y)
that is incompatible elementFigure 25.2. Helium isotope ratios in plume-derived badepleted relative to primitive
salts and MORB as a function of plume flux. There is no
mantle. As yet, there is no model
apparent relationship between plume flux and He isotope
of mantle evolution that fully
ratios. ASP = Amsterdam-St. Paul. Modified from Grareconciles noble gas and non-noble
ham (2002).
gas isotope ratios.
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Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
Iceland
Loihi
30
3He
4He
(R/RA)
Galápagos
Mauna
Loa
Juan
Fernandez
M. Kea
Koolau
CRB
Reykjanes
20 Ridge
10
Samoa
Heard
Atlantic
MORB St. Helena
0.703
Shimada
Smt
0.704
0.705
87Sr/86 Sr
African Xenoliths
Tristan
Gough
0.706
0.707
Figure 25.3. Relationship between 3He/4He and 87Sr/86Sr in mantle materials.
River Basalts. From Graham (2002).
CRB = Columbia
MODELING ATMOSPHERIC EVOLUTION
We should begin our discussion of atmospheric evolution by making the assumption, as we have for
the crust, that the Earth was initially a homogeneous body. After separation of the core, we were
left with a homogeneous silicate portion of the Earth with the composition of 'primitive mantle'.
Our working model will assume that the atmosphere, like the crust, was created from the mantle.
We shall refer to the process that created the atmosphere as degassing or outgassing. We know t h a t
the magmatism continues to outgas the mantle today. Quite possibly this is the main process by
which the atmosphere (and hydrosphere) was created. However, much of the discussion below is independent of the precise mechanism of outgassing. We shall be concerned primarily with the degree
and rate of outgassing. We should also note that this is not the only possible mechanism by which
the atmosphere was produced. One alternative hypothesis that has been suggested is production of
the atmosphere by accretion to the Earth of volatile-rich bodies such as comets after formation of t h e
Earth.
Each of the nuclides mentioned above provides a different perspective on the evolution of t h e
Earth's atmosphere. Obviously, 129Xe variations could only be produced very early in Earth's history
(within ~10 ¥ 17 = 170 Ma of nucleosynthesis, after that time the parent, 129I, had completely decayed). That variations in the ratio of 129Xe to other Xe isotopes are observed suggests (1) the Earth
formed shortly (within 170 Ma) after a nucleosynthetic event, and (2) a substantial fractionation of I
from Xe must have occurred early in Earth's history. So 129Xe variations provide clues to the early
degassing history of the Earth. He is unique because the Earth is an open system with respect to He.
4
He is continually created, while 3He is not, hence He should give us a perspective on the present degassing rate. The U-fissogenic Xe isotopes and Ar are daughters of long-lived nuclides and should integrate the entire degassing history of the Earth.
182
4/1/03
Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
Lets take a hypothetical Earth box model of
the Earth (Figure 25.4). It has the three reservoirs we have discussed before, continental
continental crust
crust (denoted C), depleted and outgassed upC
per mantle (denoted D), and undegassed and
depleted
undepleted lower mantle, or virgin mantle (V).
degassed
upper mantle
D
But for the atmophile elements we need to inmantle
clude some additional reservoirs: the atmosVO
phere (denoted A), and, since allowing for t h e
possibility that some part of the mantle has
undepleted
undegassed
been outgassed but not depleted, an outgassed,
V
mantle
lower mantle
but undepleted, or virgin, mantle (VO). The
atmosphere has substantial concentrations of
the noble gases, but no significant amounts of
Figure 25.4. Box model of the volatile inventory
the parent isotopes such as U and K; the contiof the Earth (from Allégre et al., 1986).
nental crust has substantial concentrations of U
and K but no significant amounts (we assume)
of the noble gases, the depleted and outgassed upper mantle is relatively poor in both the incompatible parents and the noble gas daughters, though the exact concentrations of both are unknown. Together, reservoirs D and VO constitute the outgassed mantle, which we denote by the subscript O. W e
will use the subscript T to denote the total system.
We can write a number of mass balance equations of the sort we introduced in Lecture 16 or used for
Nd in Lecture 18. Note that mass balance equations for intensive parameters* written for the bulk silicate Earth will also hold for bulk silicate Earth less the undegassed, undepleted, lower mantle, e.g.,
the mean concentration of Ar above the dashed line in Figure 25.4 must be the same as the concentration of Ar below the dashed line. We begin by determining the relative amount of Ar in the various
boxes. We have already noted the assumption that the amount of 36Ar in the crust is negligible.
We define the present degree of outgassing, d, as the ratio of the mass of 36Ar in the atmosphere to
the mass of 36Ar in the atmosphere plus the outgassed mantle. In other words, d is the fraction of Ar
in the atmosphere relative to the total amount of Ar above the dashed line.
atmosphere
36
d=
36
ArA
ArO + 3 6 ArA
25.2
We assume the mass of 36Ar in the continental crust is negligible. In this case, the isotopic budget for
reservoirs A and O may be written as
(4 0Ar/3 6Ar)T = d(4 0Ar/3 6Ar)A + (1 – d)(4 0Ar/3 6Ar)O
25.3
40
36
where the subscript T stands for total, or bulk Earth. Equation 25.3 says the total Ar/ Ar ratio
above the dashed line is the average of the two reservoirs, weighted by the proportion of 36Ar in
each. Rearranging equation 25.3 yields:
d=
( 4 0Ar / 3 6Ar )O –(4 0 Ar/ 3 6Ar) T
(4 0 Ar/ 3 6Ar) O –( 4 0Ar / 3 6Ar)A
25.4
We define a second value of d, d' by using (40Ar/36Ar)D instead of (40Ar/36Ar)O in 25.4:
d' =
( 4 0Ar / 3 6Ar)D –( 4 0Ar/ 3 6Ar) T
( 4 0Ar/ 3 6Ar) D –(4 0Ar / 3 6Ar)A
25.5
*
Intensive parameters are those which are independent of the mass of the system, such as concentration, isotope ratios,
temperature, etc. Extensive parameters, such as mass, heat content, amount of an element or isotope, depend on the total
mass of the system.
183
4/1/03
Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
where D stands for for depleted mantle. Since the K concentration in D is less than in O (by definition: D is depleted, part of O is not), ( 40Ar/36Ar)D ≤ ( 40Ar/36Ar)O and d' ≤ d. Assuming ( 40Ar/36Ar)D =
25,000 (typical value in undegassed MORB), (40Ar/36Ar)A = 295.5 (atmospheric), and taking the value
in Loihi seamount as representative of (40Ar/36Ar)V = (40Ar/36Ar)T = 390, we can calculate the lower
limit for d as:
d > d' =
25, 000 - 390
25,000 - 295.5
Our first conclusion then is that the depleted mantle has lost 99.6% of its 36Ar inventory.
The initial ratio of 40Ar/36Ar of the Earth can be estimated in various ways, most of which suggest a
value less than or equal to 1. 40Ar has been produced steadily throughout geologic time by decay of
40
K, and the 40Ar/36Ar has consequently increased. Because of the time-integrating character of radiogenic isotopes ratios, they should allow us to estimate the rates at which outgassing has occurred.
To understand this, imagine a choice between 2 extremely simple models of atmospheric evolution. To
make the case as simple as possible, imagine an Earth with only two reservoirs: the atmosphere and
a degassed mantle. In the first model, the atmosphere is produced by degassing of the mantle yesterday. In this case, the degassed mantle and the atmosphere should have identical 40Ar/36Ar ratios.
In model two, the atmosphere is produced when the Earth forms 4.55 Ga ago, and the atmosphere and
mantle have remained as closed systems ever since. In this case, the 40Ar/36Ar ratio of the atmosphere should be very close to the initial value (since 40K/36Ar of the atmosphere is 0, the 40Ar/36Ar
would not change with time). The 40Ar/36Ar ratio in the mantle in this model would be very high, t h e
exact value depending on the degree of outgassing and the 40K/36Ar ratio of the mantle. The a v a i l able data are not in accord with either of these simple models: the 40Ar/36Ar ratios of the mantle and
atmosphere are clearly not equal, so degassing did not occur as a single recent burp. On the other
hand, the atmospheric ratio is greater than the initial ratio, so it could not have been a closed system. Therefore we must consider more complex models.
Any model of atmospheric evolution of He, Ar or fissogenic Xe is bound to be rather complex, because
it must take account of 1.) transport of gas from mantle to atmosphere, 2.) growth of the radiogenic
isotopes in the mantle, and 3.) transport of the parent isotopes, K, U, and Th, to the crust. These sorts
of models turn out to be rather complex indeed, and we do not have time to consider them in detail.
However, the situation for 129Xe is somewhat simpler. Because of the short-half life of the parent,
129
I, we can neglect transport of 129I from mantle to crust. This is equivalent to assuming no permanent
crust formed within the first 200 Ma of Earth history, which is not an unreasonable assumption. Let's
then consider a simple model of evolution of 129Xe/130Xe ratio in the mantle and atmosphere. W h a t
we ultimately want to understand is the rate at which the mantle was degassed.
Our first task is to determine the form of the equation describing the degassing history of the mantle. We assume that degassing rate is some function of time. We must also know how degassing occurs.
Today it occurs in association with volcanism at mid-ocean ridges, which is in turn related to mantle
convection. The main driving force for all tectonic activity involving the mantle is heat, mainly h e a t
produced by radioactive decay. We can suppose that tectonic activity, such as volcanism and mantle
convection, that causes outgassing of the mantle has decreased with time as heat production has decreased, i.e., exponentially according to the radioactive decay equation. Therefore, we chose an
equation to describe the outgassing rate having an exponential form:
J0 e-bt
25.6
where J0 is the initial flux (integrated over the Earth's entire surface) and b is a rate constant analogous to the decay constant in the radioactive growth equation. If b is 0, then the degassing rate has
been constant and equal to the initial rate, J0. A very large value of b corresponds to a single burp
early catastrophic degassing. J should depend on the amount of the nuclide in the mantle (since we
expect that the more of the nuclide in the mantle, the higher the flux out of the mantle), so for 130Xe:
J0 = k1 3 0Xe0
184
25.7
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Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
where k is a constant. The rate of change of the amount of the non-radiogenic nuclide 130Xe in the mantle is then given by:
d(1 3 0Xe m,t )
= -k 1 3 0Xe m, 0e - bt
dt
25.8
where 130Xem,t is the amount of 130Xe in the mantle at time t, and 130Xem,0 is the initial amount of xenon
in the mantle. The minus sign indicates the flux is from mantle to atmosphere. The change is t h e
amount of 130Xe in the atmosphere is then just the opposite:
d(1 3 0Xe a ,t )
= k 1 3 0Xe m, 0 e -bt
dt
25.9
Integration of equations 25.8 and 25.9 yields:
È k
˘
Xe m, t = k 1 3 0Xe m, 0 Í1 + (e - bt - 1)˙
Î b
˚
k
130
Xe a ,t = 1 3 0Xe m, 0 1 - e - bt
b
130
[
25.10
]
25.11
Now if b is very small (implying catastrophic early degassing), in particular, if 1/b << 4.55 Ga, then
the exponential term approximates to 0 for t= 4.55 Ga, and equation 25.11 can be rearranged as:
k
@
b
130
Xe a
Xe m, 0
25.12
130
So for early catastrophic degassing, the k/b ratio is equal to the ratio of the 130Xe content of the a t mosphere to the initial 130Xe content of the mantle, i.e., the fraction of the 130Xe outgassed.
For a radiogenic isotope, such as 129Xe, we have the added complexity that it is being produced simultaneously with the outgassing process. The rate of change of the amount of 129Xe in the mantle is
then equal to the rate at which it is lost (degassed) plus the rate at which it is produced. We can
write this as:
d(1 2 9Xe m,t )
Ê 1 2 9Xe ˆ
= - Á 1 3 0 ˜ k 1 3 0Xe m, 0 e -bt + l 1 2 9I m,t
dt
Ë Xe ¯ m,t
We assume that
25.13
129
I is not lost from the mantle, so
129
Im,t = 1 2 9I0 e-lt
25.14
129
and
d( Xe m,t )
Ê 1 2 9Xe ˆ
= - Á 1 3 0 ˜ k 1 3 0Xe m, 0 e -bt + l 1 2 9I 0 e -lt
dt
Ë Xe ¯ m,t
25.15
We assume that atmosphere does not, and never did, contain significant amounts of iodine, so the rate
of change of 129Xe in the atmosphere is simply:
d(1 2 9Xe a, t )
Ê 1 2 9Xe ˆ
= - Á 1 3 0 ˜ k 1 3 0Xe m, 0e - bt
dt
Ë Xe ¯ m, t
25.16
We now want to consider how the 129Xe/130Xe ratio has evolved with time. For the mantle:
d(1 2 9Xe / 1 3 0Xe) m, t
l1 2 9I m,t
= 130
dt
Xe m,t
25.17
substituting equations 25.14 and 25.10 for the right side denominator and numerator respectively:
d(1 2 9Xe / 1 3 0Xe) m, t
=
dt
l1 2 9I 0 e -lt
130
Xe 0 1 + k / b (e - bt - 1)
[
185
]
25.18
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Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
For the atmosphere:
d(1 2 9Xe / 1 3 0Xe)a ,t
Ê 1 2 9Xe ˆ ¸
be -lt ÏÊ 1 2 9Xe ˆ
= - bt
ÌÁ 1 3 0 ˜ - Á 1 3 0 ˜ ˝
dt
(e - 1) ÓË Xe ¯ m,t Ë Xe ¯ a ,t ˛
25.19
Integrating these equations from 0 to T = 4.55 Ga yields the following rather messy equations:
T
129
130
( Xe / Xe )m,T0
Ê 1 2 9Xe ˆ
l1 2 9I0 0
e - lt
= Á 130 ˜ + 130
dt
Ë Xe ¯ 0
Xe 0,m Ú0 1 + k / b (e - bt - 1)
25.20
T
(1 2 9Xe /1 3 0Xe )a ,T0
l1 2 9I 0 0 - bt T0
e - lt
e
130
Ú0 1 + k / b (e - bt - 1)dtdt
Ê 1 2 9Xe ˆ
Xe 0, m Ú0
= Á 130 ˜ +
Ë Xe ¯ 0
(e - T0 t - 1) / b
25.21
Both these equations have the form 129Xe/130Xe = initial + radiogenic; the radiogenic component is t h e
last term in both cases. We define the ratio of the radiogenic component in the 129Xe/130Xe ratio (i.e.,
in our usual notation 129Xe*/130Xe) of the mantle and atmosphere as R:
ÏÊ 1 2 9Xe ˆ
Ê 1 2 9 Xe * ˆ
Ê 1 2 9Xe ˆ ¸
Á 130
˜
˜
Á
˜ Ô
ÔÁ
Xe ¯ m,T ÔË 1 3 0Xe ¯ m,T Ë 1 3 0Xe ¯ 0 Ô
Ë
R = 129
= Ì 129
˝
Ê Xe *ˆ
Ê Xe ˆ
Ê 1 2 9Xe ˆ Ô
Ô
Á 130
˜
Á
˜ -Á
˜
Xe ¯ a ,T ÔÓ Ë 1 3 0Xe ¯ a ,T Ë 1 3 0Xe ¯ 0 Ô˛
Ë
25.22
This is the ratio of the last terms on the right in
R
0.999
1.0
0.99
equations 25.20 and 25.21. We can see that these
1000
terms are functions of b, and k/b only (the
k
0.95
129
b
I/130Xe0 terms, terms for the initial 129I/130Xe of
0.9
the Earth, which are also unknown, cancel).
0.8
0.6
Staudacher and Allègre (1982) took the ap100
0.2
proach of solving for R through numerical integration using various values of b and k/b. The
results are plotted in figure 25.5, which shows R
as a function of b with curves drawn for various
10
values of k/b. R can be independently estimated
from the present 129Xe/130Xe ratios of the atmosphere and degassed mantle if we can estimate
the initial ratio (equation 25.22). Staudacher
1
and Allègre estimated the initial 129Xe/130Xe as
10-7
10 -6
10-5
10 -9
10-8
6.34 from the solar wind value (the Sun would
b
have had a very low ( 129I/130Xe)0 ratio because,
Figure 25.5 Ratio of 129Xe*/130Xe in the mantle to
unlike the Earth, it did not loose Xe relative to I
129
Xe*/130Xe in the atmosphere as a function of b,
when it formed; as a result, the present solar rathe degassing rate constant and k/b, the fraction
tio should be similar to the initial terrestrial
of xenon degassed from the mantle.
ratio). The atmospheric value is 6.48 and t h e
129
130
mantle value is estimated from the highest Xe/ Xe observed, which is 7.09. R is then estimated
as:
Ï 7.09 - 6.34 ¸
R =Ì
˝ = 5.4
Ó 6.48 - 6.34 ˛
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Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
Recall that the ratio k/b approximates to the fraction of 130Xe outgassed from the mantle. This can be
independently estimated as about 0.5-0.6 (i.e., the mantle has lost 50-60% of its xenon). In Figure 25.5
the value of b corresponding to R= 5.4 and k/b = 0.5 is about 10-7 yr-1. This value of b corresponding to
releasing about 1/2 the 130Xe now in the atmosphere in about 7 million years. In other words, it implies a rather rapid early degassing. Notice that, at least in a qualitative sense, this result is very
robust. Even if R were as low as 1.5 or as high as 100, if t h e
1010
fraction of xenon outgassed is anywhere between 20% and
10
10
100%, we still find a value of b between 10-8 and 10-6 yr-1, im107
plying early catastrophic degassing.
36Ar 8
108
10
This sort of early catastrophic degassing is difficult to recflux
oncile with the amount of radiogenic 40Ar observed in the a t 106
6
g/a
mosphere, which seems to require some later degassing (i.e.,
10
after some of the 40K had decayed to produce 40Ar). There10 Ma 30
fore, Allègre et al. (1986) have proposed a more complex degassing function of the form:
J = J0 {(1 - b)e -bt + be - gt }
25.23
where b and g are additional constants, with the value of g
being much shorter than that of b. Allègre et al. suggested
appropriate values for b, b, and g are 10-3, 3 ¥ 10-7yr-1, and 2 ¥
10-9yr-1 respectively. This equation produces degassing fluxes
through time as shown in Figure 25.6: an initial 'big burp' followed by slowly decreasing less intense degassing. We can
interpret the 'big burp' as being a result of extensive melting
of the mantle which may have occurred as a result heating
due to release of gravitational energy during accretion and
perhaps from decay of 26Al, which may have been abundant
in the early Earth, if it formed early enough, as well. Subsequent, less intense degassing would result from volcanism,
such as mid-ocean ridge volcanism today. Equation 25.23
still retains an early catastrophic term. Note that 129Xe
would be insensitive to the second term in 25.23 because it a l l
the 129I decays very early when the equation is still dominated by the first term.
A number of workers have produced atmospheric evolution
models and they differ from the Allègre et al. model we
have discussed here in various details (e.g., Damon and
Kulp, 1958, Ozima and Alexander, 1976, Hart, et al., 1985).
However, they are generally consistent in concluding t h a t
there was an early phase of rapid degassing and that about
1/2 half the mantle has been degassed.
Ne Isotope Ratios
Ne isotope ratios of MORB and OIB are distinct from those
of the atmosphere (Figure 25.7). This might at first seem
perplexing , since there are no radioactive nuclides decaying
to any of the Ne isotopes (20Ne, 21Ne, and 22Ne). Variation in
21
Ne is due to several nuclear reactions, such as 18O (a,n) 21Ne
or 24Mg (n,a) 21Ne (the a and n coming from a decay and fission). These reactions produced significant variations in t h e
21
Ne/22Ne ratio in the mantle since 21Ne is a very rare nuclide
(0.26% of Ne), and the abundance of Ne in the mantle is very
187
5
4
3
2
1
0
4
3
2
1
0
4He
1020
1
flux 0.5
g/a 0.1
4
40Ar
1010
4
3
2
1
3
flux 2
g/a 1
10
4
129Xe
105
2
radiogenic
gas
2
30
1
0
2
1
flux 1
g/a
0
3
Ma
10 40
Ma
4
3
2
age (Ga)
1
0
Figure 25.6. Fluxes of noble gases to
the atmosphere as a function of time
based on equation 25.22 and the v a l ues of b, b, and g given in the text.
4/1/03
Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
low. In the atmosphere, Ne is much
more abundance and these reactions are
uncommon, so there is no significant
variation in 21Ne/22Ne.
The variation in 20Ne/22Ne is more
difficult to account for.
Sarda et al
(1988) have suggested the following scenario (illustrated in Figure 25.8) to account for these variations. They note
that the atmosphere has Ne isotope ratios that differ from those of the Sun.
They suggest Ne was largely lost from
any early primitive terrestrial atmosphere, and extensive mass fractionation
occurred during this processes (driving
the 20Ne/22Ne and 21Ne/22Ne down along
a line with slope = 2 in Figure 25.8). The
Figure 25.7. Ne isotope variations in some oceanic basalts,
Ne in the mantle at that time, however,
including MORB and seamounts associated with the H a did not suffer this fractionation and rewaiian and Society mantle plumes. ‘MDF’ is the mass detained “solar" Ne isotopic composition.
21
pendent fractionation line.
Over time, Ne was produced in t h e
mantle by the reactions mentioned
above, driving the mantle isotope ratio
horizontally to the right in Figure 25.8.
(It is also possible to produce 20Ne by
these same reactions with different targets, but because 20Ne is so much more
abundant, the affect on the 20Ne/22Ne
ratio would be insignificant.) OIB, in
their model, are derived from a less degassed reservoir in which the nucleogenic component of 21Ne is less significant, and they are not shifted as far
away from the “solar” value.
Figure 25.8. Model for the variation of Ne isotope ratios in
Contamination of the basalts by atthe Earth. The atmospheric ratios decrease relative to somospheric gases, during, before, or after
lar values along a mass-dependent fractionation line during
eruption then shifts values of individloss of Ne from early atmosphere. 21Ne is produced in t h e
ual MORB and OIB toward the atmosmantle by (a, n) and (n,a) reactions. Variations observed in
pheric composition along lines labeled
MORB and OIB represent mixing between this ‘degassed
mixing.
mantle’ Ne and atmospheric Ne as a result of contamination
One might ask how it is that the manduring eruption.
tle can remain so distinct in it’s isotopic
composition of atmophile elements if
surface material is continually recycled to the mantle in subduction zones. The answer seems to be
that the subducting slab is thoroughly degassed (about 98%) in the early stages of subduction
(Staudacher and Allègre, 1988). This probably occurs through a combination of ‘dewatering’ of sediments as they are initially compressed in the trench, and dehydration (which we should more accurately call devolatilization, particularly in this context) during the first 100 km of descent.
References and Suggestions for Further Reading:
Allègre, C. J., T. Staudacher, and P. Sarda, Rare gas systematics: formation of the atmosphere, evolution and structure of the Earth's mantle, Earth. Planet. Sci. Lett., 81, 127-150, 1986.
188
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Geol. 656 Isotope Geochemistry
Lecture 25
Spring 2003
Damon, P. E., and J. L. Kulp, Inert gases and the evolution of the atmosphere, Geochim. Cosmochim.
Acta, 13, 280- , 1958.
Davies, G. F. , 1988. Ocean bathymetry and mantle convection, 1, large-scale flow and hotspots, J.
Geophys. Res., 93:10467-10480.
Farley, K. A. and H. Craig. 1992. Atmospheric argon contamination of oceanic island basalt olivine
phenocrysts. Geochim. Cosmochim. Acta. 58: 2519-2526.
Farley, K. A. and R. J. Poreda. 1993. Mantle neon and atmospheric contamination. Earth Planet. Sci.
Lett. 114: 325-339.
Farley, K. A., J. H. Natland and H. Craig. 1992. Binary mixing of enriched and undegassed (primitive ?) mantle components (He, Sr, Nd, Pb) in Samoan lavas. Earth Planet. Sci. Lett. 111: 183-199.
Graham, D.,Noble gas isotope geochemistry of mid-ocean ridge and oceanic island basalts: characterization of mantle source reservoirs, in D. Porcelli, et al. (ed.), Noble Gases in Geochemistry and
Cosmochemistry, 247-218, 2002.
Hart, R., L. Hogan, and J. Dymond, The closed-system approximation for evolution of argon and h e lium in the mantle, crust and atmosphere, Chem. Geol., 52, 45-73, 1985.
Ozima, M., Noble gas state in the mantle, Rev. Geophys., 32:405-426, 1994.
Ozima, M. and E. C. Alexander, Rare gas fractionation patterns in terrestrial samples and the Earth
atmosphere evolution model, Rev. Geophys. Space Phys., 14, 386- , 1976.
Sleep, N. H., 1990. Hotspots and Mantle Plumes: some phenomenology, J. Geophys. Res., 95:6715-6736.
Staudacher, T. and C. J. Allègre, Recycling of oceanic crust and sediments: the noble gas subduction
barrier, Earth. Planet. Sci. Lett., 89, 173-183, 1988.
Staudacher, T. and C. J. Allègre, Terrestrial xenology, Earth. Planet. Sci. Lett., 60, 389-406, 1982.
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